For a three-act plot analysis, put on your screenwriter’s hat. Moviemakers know the formula well: at the end of Act One, the main character is drawn in completely to a conflict. During Act Two, she is farthest away from her goals. At the end of Act Three, the story is resolved.
Act I
The narrator begins working as a Handmaid to a Commander and gradually becomes more involved with him, while also trying to find her way into the resistance and battling with flashbacks from her past.
Act II
The narrator's secret relationship with the Commander switches from being about Scrabble to being about sex. When she's with him at Jezebel's she runs into an old friend, Moira, whose experience shows that their society is tough on all women at that point. She also begins having sex with the house chauffeur, Nick.
Each of these relationships is illegal and secret—the Commander's Wife can't know about her relationship with the Commander and the Commander can't know that his Wife is making her sleep with Nick. The narrator realizes that she may be pregnant with Nick's child.
Act III
The narrator has to attend a Salvaging (execution), where her friend Ofglen, also in the resistance, is compromised. Ofglen disappears and the narrator learns that she killed herself. The narrator realizes that she too may be in danger. We learn that the Commander's Wife has found out about the narrator and the Commander. The narrator is waiting for the axe to fall when some men dressed as government agents come to arrest her. Nick says they're from the resistance, but who knows? The narrator goes with them and we never find out what happens to her.